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A Physical Model for the Dot Product: Does it Improve Learning of Vector Mechanics?

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2012 ASEE Annual Conference & Exposition


San Antonio, Texas

Publication Date

June 10, 2012

Start Date

June 10, 2012

End Date

June 13, 2012



Conference Session

Mechanics Concepts I

Tagged Division


Page Count


Page Numbers

25.86.1 - 25.86.8

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Paper Authors


Luciano Fleischfresser Universidade Tecnológica Federal do Paraná Orcid 16x16

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Luciano Fleischfresser is an Associate Professor at Universidade Tecnológica Federal do Paraná, where he teaches the vector mechanics sequence (statics and dynamics) for engineering majors. Fleischfresser holds a Ph.D. from the University of Oklahoma's School of Meteorology and bachelor's/master's degrees in mechanical engineering from Universidade Federal do Paraná and Universidade Federal do Santa Catarina respectively. His research interests are in engineering educational research and in environmental fluid mechanics.

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Mariana Nascimento Casarin Universidade Tecnológica Federal do Paraná

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Mariana Nascimento Casarin was born in Campo Mourão, Paraná. She graduated with honors from the high school computer technical program offered at Universidade Tecnológica Federal do Paraná, Campo Mourão xampus (UTFPR – CM), in 2011. She is now enrolled as a freshman in the electronic engineering program at the same institution.

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Evandro Eizo Roncaglia Yabushita Universidade Tecnológica Federal do Paraná

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Evandro Eizo Roncaglia Yabushita was born in Maringá, PR, and he lived in the town of Santa Fé until he was 18 years old. He was admitted to Universidade Tecnológica Federal do Paraná, Campo Mourão campus (UTFPR-CM), in 2008. Currently, Roncaglia Yabushita is a junior in the environmental engineering program.

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The use of physical models in Engineering Mechanics – Statics classesIn an effort to verify if the use of physical models of statics problems help improve problem-solving skills, we report on a preliminary study with an engineering class of 43 pupils. Thequestion being investigated relates to the ability of performing the scalar product of vectorsefficiently and to understand it as a projection of one vector in another direction. The mainresults are: 1. From the 11 students that missed class on the day the prototype was shown and the problem solved on the chalkboard, no one solved the question correctly on test day; 2. From the other 32 students in class, 18 got the question right and 14 did not; 3. The most common mistake among all students (the ones that missed class and the ones that did not) was to keep unit vectors on the answer after performing the scalar product, that is, they reported the answer as a vector and not as a scalar (44% of the class); 4. Of the 18 students answering the question right, 9 were males and 9 females, showing no evidence of gender preference; 5. Only 2 students attempted to solve the problem based on how they learned scalar product in a previous math class (without unit vectors), and they both made mistakes.One possible cause for the high percentage of students missing the question on test day maybe the time lag between the day when the model was shown and the day students took the test(2 weeks).We plan to use three other physical models (already built) throughout this semester: one forequilibrium; one for plane truss analysis using the method of sections; and one for a spatialtruss using the method of nodes. The approach will again be to present the model in class,show the solution on board, and ask students to solve a similar problem on test day.Previous studies have shown mixed results when it comes to verify problem-solving skillsimprovement with the use of hands-on statics education. Our goal is to verify if spatialvisualization and mathematical skills can be improved when 3-D objects are used tocomplement chalk drawings and solutions. Figure: Physical model to demonstrate scalar productRelevant Reference: Hands-on-Statics Integration into an Engineering Mechanics- Statics Course: Development and Scaling Jack LeskoA, Jack DukeA, Seigfried HolzerB, Flynn AucheyC A Department of Engineering Science & Mechanics B Via Department of Civil & Environmental Engineering C Department of Building Construction Virginia Tech Blacksburg, Virginia 24061 Proceedings of the 1999 American Society for Engineering Education Annual Conference & Exposition Section 1368

Fleischfresser, L., & Casarin, M. N., & Roncaglia Yabushita, E. E. (2012, June), A Physical Model for the Dot Product: Does it Improve Learning of Vector Mechanics? Paper presented at 2012 ASEE Annual Conference & Exposition, San Antonio, Texas.

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